Find the value of a for which Find the value of a for which

Find the value of a for which

Find the value of a for which v = [-1 a -12 -5] is in the set

Solution

so v is in span of H

so then v = dv1+bv2+cv3 [ v1 ,v2,v3 are vectors given in the H , d,b,c are constant]

now plug the values into this

then comparing the first row values we get d = 1

a =-2-4b

a= -2 -4b

now comparing third row value

-12 = -5 -3b-5c

-7 = -3b-5c

3b+5c=7 ---->1

comparing 4th row values

-5 = 2+b-3c

b -3c =-7 --->

solving 1 and 2 we get b =-1 and c=2

but a = -2-4b = -2 - 4(-1) = -2 +4 =2